Experimentally observed deviations from ideal isothermal behavior of solid electrolyte sensors are explained on the basis of gas-phase diffusion in the furnace atmosphere. The presence of small amounts of CO/CO2 or other oxygenbearing gas species is essential to the theoretical explanation of these effects. Solution of the basic transport equations for limiting conditions appropriate to the control of a stagnant atmosphere by a sensor/pump combination indicates that stable fugacity fronts may exist, separating regions of relatively uniform oxygen fugacity which differ from each other by many orders of magnitude. The position of the front depends on the oxygen fugacity difference between the two regions of the furnace and can be moved through the furnace by electrochemically pumping oxygen from one end of the furnace. The relative output of two sensors separated by some finite distance in the direction in the direction of oxygen transport will depend on the position of this front, and as the front passes between the sensors a plateau in the curve of one sensor emf versus the other is predicted.